Question

What is the arc length if Θ = 2 pi over 7 and the radius is 3 cm?

Answer 1

7 pi over 12

12 pi over 7

6 pi over 7

7 pi over 6

Answer 2

@campbell_st

Answer 3

well isn't arc length

\[l = \theta \times r\]

so multiply that angle by the radius

Answer 4

How is it not arc length? So, it would be L= 2pi/7 x 3?

Answer 5

well I said..."isn't arc length"

Answer 6

that's correct... you just need to simplify it

Answer 7

yeah, im not really good at that :( sorry, it never caught on

Answer 8

thats ok.. so what answer do you think...?

Answer 9

I guessing 6pi/7 ?

Answer 10

great guess

Answer 11

lol, yaay! thank you

Answer 12

glad to help

Answer 13

Question though, how do you solve that? Like changing a radian into a degree and vice versa?

Answer 14

assuming the angle is in radians.... you should say so.

r =3cm, diameter = 6 cm and circum = 6π
arc length = circum(angle/2π)
.......use this formula to get your answer...........

Answer 15

ok... so you need to know

\[180^o = \pi\]

so

\[1^o = \frac{\pi}{180}\]

and with radians

\[1^r = \frac{180}{\pi}\]

so as a simple explanation...

an equalateral triangle has all sides equation and all angles 60

imagine a sector when the 2 radii and the arc are the same length...

its like pushing on 2 vertices of an equlilateral and bending the 3rd side to make an arc...

the angle goes from 60 to a value a bit less than 60... and its called a radian...

so 1 radian = 57.29 degrees.... so by bending the side out... the angle has to get smaller..

hope that's not 2 confusing

Answer 16

kind of, yeah.

Answer 17

well just remember

180 = pi.... and then just manipulate that

Answer 18

Ok, so if I have 90 degrees and want to change it into a radian I would use 180/pi?

Answer 19

so divide both sides by 2

\[\frac{180}{2} = \frac{\pi}{2} ...or.... 90^o = \frac{\pi}{2}\]

Answer 20

45?

Answer 21

ok.... so 45 is half of 90.. so divide the previous by 2

\[\frac{90}{2} = \frac{\frac{\pi}{2}}{2}.... or...... 45 = \frac{\pi}{4}\]

Answer 22

11.25?

Answer 23

wait, is pi/4 the answer?

Answer 24

thats it... where ever possible leave the angle in terms of pi

Answer 25

oh ok! Thanks for explaining, I'm a little rusty but I think I get it

Answer 26

Can you help with another question? It's about amplitude and periods etc

Answer 27

ok... just post it... as a new question... and there are plenty of people who can help

Answer 28

ok thanks.

Answer 29

Thanku soo much!! :D

Answer 30

@malice ;)

Answer 31

@malice this is how i found u hehe

Answer 32

LOL cool haha :D

Answer 33

I can't believe that I have already finished this course... *sniff*
^-^

Answer 34

Life really does go on.............

Answer 35

@malice im still finishing it